Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Percentage Accurate: 99.8% → 99.8%

Time: 7.2s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - ((y + 0.5d0) * log(y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * Math.log(y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - ((y + 0.5) * math.log(y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(Float64(y + 0.5) * log(y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - ((y + 0.5) * log(y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \log y \cdot \left(0.5 + y\right)\right) + y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (log y) (+ 0.5 y))) y) z))

C

double code(double x, double y, double z) {
	return ((x - (log(y) * (0.5 + y))) + y) - z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x - (log(y) * (0.5d0 + y))) + y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x - (Math.log(y) * (0.5 + y))) + y) - z;
}

Python

def code(x, y, z):
	return ((x - (math.log(y) * (0.5 + y))) + y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - Float64(log(y) * Float64(0.5 + y))) + y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x - (log(y) * (0.5 + y))) + y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - N[(N[Log[y], $MachinePrecision] * N[(0.5 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto \left(\left(x - \log y \cdot \left(0.5 + y\right)\right) + y\right) - z \]
4. Add Preprocessing

Alternative 2: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 \cdot x + \left(y - z\right)\\ t_1 := \left(x - \log y \cdot \left(0.5 + y\right)\right) + y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+122}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 345:\\ \;\;\;\;-0.5 \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 1.0 x) (- y z))) (t_1 (+ (- x (* (log y) (+ 0.5 y))) y)))
   (if (<= t_1 -5e+122)
     (* (- 1.0 (log y)) y)
     (if (<= t_1 -1000000.0)
       t_0
       (if (<= t_1 345.0) (- (* -0.5 (log y)) z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 * x) + (y - z);
	double t_1 = (x - (log(y) * (0.5 + y))) + y;
	double tmp;
	if (t_1 <= -5e+122) {
		tmp = (1.0 - log(y)) * y;
	} else if (t_1 <= -1000000.0) {
		tmp = t_0;
	} else if (t_1 <= 345.0) {
		tmp = (-0.5 * log(y)) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (1.0d0 * x) + (y - z)
    t_1 = (x - (log(y) * (0.5d0 + y))) + y
    if (t_1 <= (-5d+122)) then
        tmp = (1.0d0 - log(y)) * y
    else if (t_1 <= (-1000000.0d0)) then
        tmp = t_0
    else if (t_1 <= 345.0d0) then
        tmp = ((-0.5d0) * log(y)) - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 * x) + (y - z);
	double t_1 = (x - (Math.log(y) * (0.5 + y))) + y;
	double tmp;
	if (t_1 <= -5e+122) {
		tmp = (1.0 - Math.log(y)) * y;
	} else if (t_1 <= -1000000.0) {
		tmp = t_0;
	} else if (t_1 <= 345.0) {
		tmp = (-0.5 * Math.log(y)) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 * x) + (y - z)
	t_1 = (x - (math.log(y) * (0.5 + y))) + y
	tmp = 0
	if t_1 <= -5e+122:
		tmp = (1.0 - math.log(y)) * y
	elif t_1 <= -1000000.0:
		tmp = t_0
	elif t_1 <= 345.0:
		tmp = (-0.5 * math.log(y)) - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 * x) + Float64(y - z))
	t_1 = Float64(Float64(x - Float64(log(y) * Float64(0.5 + y))) + y)
	tmp = 0.0
	if (t_1 <= -5e+122)
		tmp = Float64(Float64(1.0 - log(y)) * y);
	elseif (t_1 <= -1000000.0)
		tmp = t_0;
	elseif (t_1 <= 345.0)
		tmp = Float64(Float64(-0.5 * log(y)) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 * x) + (y - z);
	t_1 = (x - (log(y) * (0.5 + y))) + y;
	tmp = 0.0;
	if (t_1 <= -5e+122)
		tmp = (1.0 - log(y)) * y;
	elseif (t_1 <= -1000000.0)
		tmp = t_0;
	elseif (t_1 <= 345.0)
		tmp = (-0.5 * log(y)) - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 * x), $MachinePrecision] + N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x - N[(N[Log[y], $MachinePrecision] * N[(0.5 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+122], N[(N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -1000000.0], t$95$0, If[LessEqual[t$95$1, 345.0], N[(N[(-0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) < -4.99999999999999989e122

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - -1 \cdot \log \left(\frac{1}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - -1 \cdot \log \left(\frac{1}{y}\right)\right) \cdot y} \]

      2. mul-1-neg N/A

         \[\leadsto \left(1 - \color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right)}\right) \cdot y \]

      3. log-rec N/A

         \[\leadsto \left(1 - \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log y\right)\right)}\right)\right)\right) \cdot y \]

      4. remove-double-neg N/A

         \[\leadsto \left(1 - \color{blue}{\log y}\right) \cdot y \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \log y\right) \cdot y} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \log y\right)} \cdot y \]

      7. lower-log.f64 65.0

         \[\leadsto \left(1 - \color{blue}{\log y}\right) \cdot y \]

   5. Applied rewrites 65.0%

      \[\leadsto \color{blue}{\left(1 - \log y\right) \cdot y} \]

   if -4.99999999999999989e122 < (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) < -1e6 or 345 < (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y)

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right) - z} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right)} - z \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

      5. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right)} + \left(y - z\right) \]

      6. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right)\right)} + \left(y - z\right) \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right) + x\right)} + \left(y - z\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right) \cdot \log y}\right)\right) + x\right) + \left(y - z\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right)\right) \cdot \log y} + x\right) + \left(y - z\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right), \log y, x\right)} + \left(y - z\right) \]

      11. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right)}\right), \log y, x\right) + \left(y - z\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{2} + y\right)}\right), \log y, x\right) + \left(y - z\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, \log y, x\right) + \left(y - z\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2}} - y, \log y, x\right) + \left(y - z\right) \]

      17. lower--.f64 99.9

          \[\leadsto \mathsf{fma}\left(-0.5 - y, \log y, x\right) + \color{blue}{\left(y - z\right)} \]

   4. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 - y, \log y, x\right) + \left(y - z\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right)} + \left(y - z\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right) \cdot x} + \left(y - z\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right) \cdot x} + \left(y - z\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x} + 1\right)} \cdot x + \left(y - z\right) \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right)\right)} + 1\right) \cdot x + \left(y - z\right) \]

      5. associate-/l* N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\log y \cdot \frac{\frac{1}{2} + y}{x}}\right)\right) + 1\right) \cdot x + \left(y - z\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\frac{\frac{1}{2} + y}{x} \cdot \log y}\right)\right) + 1\right) \cdot x + \left(y - z\right) \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{\frac{1}{2} + y}{x}\right)\right) \cdot \log y} + 1\right) \cdot x + \left(y - z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\frac{\frac{1}{2} + y}{x}\right), \log y, 1\right)} \cdot x + \left(y - z\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(\left(\frac{1}{2} + y\right)\right)}{x}}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot \left(\frac{1}{2} + y\right)}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1 \cdot \left(\frac{1}{2} + y\right)}{x}}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot \frac{1}{2} + -1 \cdot y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2}} + -1 \cdot y}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{-1}{2} + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2} - y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      16. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2} - y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      17. lower-log.f64 96.3

          \[\leadsto \mathsf{fma}\left(\frac{-0.5 - y}{x}, \color{blue}{\log y}, 1\right) \cdot x + \left(y - z\right) \]

   7. Applied rewrites 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-0.5 - y}{x}, \log y, 1\right) \cdot x} + \left(y - z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x + \left(y - z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 86.1%

       \[\leadsto 1 \cdot x + \left(y - z\right) \]

   if -1e6 < (+.f64 (-.f64 x (*.f64 (+.f64 y #s(literal 1/2 binary64)) (log.f64 y))) y) < 345

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y - \left(z + \log y \cdot \left(\frac{1}{2} + y\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{y - \left(z + \log y \cdot \left(\frac{1}{2} + y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y - \color{blue}{\left(\log y \cdot \left(\frac{1}{2} + y\right) + z\right)} \]

      3. *-commutative N/A

         \[\leadsto y - \left(\color{blue}{\left(\frac{1}{2} + y\right) \cdot \log y} + z\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y - \color{blue}{\mathsf{fma}\left(\frac{1}{2} + y, \log y, z\right)} \]

      5. lower-+.f64 N/A

         \[\leadsto y - \mathsf{fma}\left(\color{blue}{\frac{1}{2} + y}, \log y, z\right) \]

      6. lower-log.f64 100.0

         \[\leadsto y - \mathsf{fma}\left(0.5 + y, \color{blue}{\log y}, z\right) \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{y - \mathsf{fma}\left(0.5 + y, \log y, z\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \color{blue}{\left(z + \frac{1}{2} \cdot \log y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 98.7%

      \[\leadsto -0.5 \cdot \log y - \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \log y \cdot \left(0.5 + y\right)\right) + y \leq -5 \cdot 10^{+122}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y\\ \mathbf{elif}\;\left(x - \log y \cdot \left(0.5 + y\right)\right) + y \leq -1000000:\\ \;\;\;\;1 \cdot x + \left(y - z\right)\\ \mathbf{elif}\;\left(x - \log y \cdot \left(0.5 + y\right)\right) + y \leq 345:\\ \;\;\;\;-0.5 \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x + \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 \cdot x + \left(y - z\right)\\ \mathbf{if}\;x \leq -11000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;-0.5 \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* 1.0 x) (- y z))))
   (if (<= x -11000.0) t_0 (if (<= x 3.5e+17) (- (* -0.5 (log y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 * x) + (y - z);
	double tmp;
	if (x <= -11000.0) {
		tmp = t_0;
	} else if (x <= 3.5e+17) {
		tmp = (-0.5 * log(y)) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 * x) + (y - z)
    if (x <= (-11000.0d0)) then
        tmp = t_0
    else if (x <= 3.5d+17) then
        tmp = ((-0.5d0) * log(y)) - z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 * x) + (y - z);
	double tmp;
	if (x <= -11000.0) {
		tmp = t_0;
	} else if (x <= 3.5e+17) {
		tmp = (-0.5 * Math.log(y)) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 * x) + (y - z)
	tmp = 0
	if x <= -11000.0:
		tmp = t_0
	elif x <= 3.5e+17:
		tmp = (-0.5 * math.log(y)) - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 * x) + Float64(y - z))
	tmp = 0.0
	if (x <= -11000.0)
		tmp = t_0;
	elseif (x <= 3.5e+17)
		tmp = Float64(Float64(-0.5 * log(y)) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 * x) + (y - z);
	tmp = 0.0;
	if (x <= -11000.0)
		tmp = t_0;
	elseif (x <= 3.5e+17)
		tmp = (-0.5 * log(y)) - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 * x), $MachinePrecision] + N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -11000.0], t$95$0, If[LessEqual[x, 3.5e+17], N[(N[(-0.5 * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -11000 or 3.5e17 < x

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right) - z} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right)} - z \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

      4. lower-+.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

      5. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right)} + \left(y - z\right) \]

      6. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right)\right)} + \left(y - z\right) \]

      7. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right) + x\right)} + \left(y - z\right) \]

      8. lift-*.f64 N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right) \cdot \log y}\right)\right) + x\right) + \left(y - z\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right)\right) \cdot \log y} + x\right) + \left(y - z\right) \]

      10. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right), \log y, x\right)} + \left(y - z\right) \]

      11. lift-+.f64 N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right)}\right), \log y, x\right) + \left(y - z\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{2} + y\right)}\right), \log y, x\right) + \left(y - z\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, \log y, x\right) + \left(y - z\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

      15. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2}} - y, \log y, x\right) + \left(y - z\right) \]

      17. lower--.f64 99.8

          \[\leadsto \mathsf{fma}\left(-0.5 - y, \log y, x\right) + \color{blue}{\left(y - z\right)} \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 - y, \log y, x\right) + \left(y - z\right)} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right)} + \left(y - z\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right) \cdot x} + \left(y - z\right) \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right) \cdot x} + \left(y - z\right) \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x} + 1\right)} \cdot x + \left(y - z\right) \]

      4. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right)\right)} + 1\right) \cdot x + \left(y - z\right) \]

      5. associate-/l* N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\log y \cdot \frac{\frac{1}{2} + y}{x}}\right)\right) + 1\right) \cdot x + \left(y - z\right) \]

      6. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\frac{\frac{1}{2} + y}{x} \cdot \log y}\right)\right) + 1\right) \cdot x + \left(y - z\right) \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{\frac{1}{2} + y}{x}\right)\right) \cdot \log y} + 1\right) \cdot x + \left(y - z\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\frac{\frac{1}{2} + y}{x}\right), \log y, 1\right)} \cdot x + \left(y - z\right) \]

      9. distribute-neg-frac N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(\left(\frac{1}{2} + y\right)\right)}{x}}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot \left(\frac{1}{2} + y\right)}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      11. lower-/.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1 \cdot \left(\frac{1}{2} + y\right)}{x}}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      12. distribute-lft-in N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot \frac{1}{2} + -1 \cdot y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2}} + -1 \cdot y}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{\frac{-1}{2} + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      15. unsub-neg N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2} - y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      16. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2} - y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

      17. lower-log.f64 99.8

          \[\leadsto \mathsf{fma}\left(\frac{-0.5 - y}{x}, \color{blue}{\log y}, 1\right) \cdot x + \left(y - z\right) \]

   7. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-0.5 - y}{x}, \log y, 1\right) \cdot x} + \left(y - z\right) \]

   8. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x + \left(y - z\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 72.5%

       \[\leadsto 1 \cdot x + \left(y - z\right) \]

   if -11000 < x < 3.5e17

   1. Initial program 99.8%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y - \left(z + \log y \cdot \left(\frac{1}{2} + y\right)\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \color{blue}{y - \left(z + \log y \cdot \left(\frac{1}{2} + y\right)\right)} \]

      2. +-commutative N/A

         \[\leadsto y - \color{blue}{\left(\log y \cdot \left(\frac{1}{2} + y\right) + z\right)} \]

      3. *-commutative N/A

         \[\leadsto y - \left(\color{blue}{\left(\frac{1}{2} + y\right) \cdot \log y} + z\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto y - \color{blue}{\mathsf{fma}\left(\frac{1}{2} + y, \log y, z\right)} \]

      5. lower-+.f64 N/A

         \[\leadsto y - \mathsf{fma}\left(\color{blue}{\frac{1}{2} + y}, \log y, z\right) \]

      6. lower-log.f64 99.8

         \[\leadsto y - \mathsf{fma}\left(0.5 + y, \color{blue}{\log y}, z\right) \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{y - \mathsf{fma}\left(0.5 + y, \log y, z\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \color{blue}{\left(z + \frac{1}{2} \cdot \log y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 62.1%

      \[\leadsto -0.5 \cdot \log y - \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.205:\\ \;\;\;\;\mathsf{fma}\left(-0.5, \log y, x\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - \log y \cdot y\right) + y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.205) (- (fma -0.5 (log y) x) z) (- (+ (- x (* (log y) y)) y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.205) {
		tmp = fma(-0.5, log(y), x) - z;
	} else {
		tmp = ((x - (log(y) * y)) + y) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.205)
		tmp = Float64(fma(-0.5, log(y), x) - z);
	else
		tmp = Float64(Float64(Float64(x - Float64(log(y) * y)) + y) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.205], N[(N[(-0.5 * N[Log[y], $MachinePrecision] + x), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x - N[(N[Log[y], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.204999999999999988

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - \left(z + \frac{1}{2} \cdot \log y\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x - \color{blue}{\left(\frac{1}{2} \cdot \log y + z\right)} \]

      2. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - \frac{1}{2} \cdot \log y\right) - z} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \frac{1}{2} \cdot \log y\right) - z} \]

      4. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \log y\right)\right)\right)} - z \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{2} \cdot \log y\right)\right) + x\right)} - z \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \log y} + x\right) - z \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} \cdot \log y + x\right) - z \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2}, \log y, x\right)} - z \]

      9. lower-log.f64 99.3

         \[\leadsto \mathsf{fma}\left(-0.5, \color{blue}{\log y}, x\right) - z \]

   5. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5, \log y, x\right) - z} \]

   if 0.204999999999999988 < y

   1. Initial program 99.7%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \left(\left(x - \color{blue}{-1 \cdot \left(y \cdot \log \left(\frac{1}{y}\right)\right)}\right) + y\right) - z \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(x - -1 \cdot \color{blue}{\left(\log \left(\frac{1}{y}\right) \cdot y\right)}\right) + y\right) - z \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(-1 \cdot \log \left(\frac{1}{y}\right)\right) \cdot y}\right) + y\right) - z \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right)} \cdot y\right) + y\right) - z \]

      4. log-rec N/A

         \[\leadsto \left(\left(x - \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log y\right)\right)}\right)\right) \cdot y\right) + y\right) - z \]

      5. remove-double-neg N/A

         \[\leadsto \left(\left(x - \color{blue}{\log y} \cdot y\right) + y\right) - z \]

      6. lower-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\log y \cdot y}\right) + y\right) - z \]

      7. lower-log.f64 99.4

         \[\leadsto \left(\left(x - \color{blue}{\log y} \cdot y\right) + y\right) - z \]

   5. Applied rewrites 99.4%

      \[\leadsto \left(\left(x - \color{blue}{\log y \cdot y}\right) + y\right) - z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+81}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, \log y, x\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, \log y, y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e+81) (- (fma -0.5 (log y) x) z) (- (fma (- y) (log y) y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e+81) {
		tmp = fma(-0.5, log(y), x) - z;
	} else {
		tmp = fma(-y, log(y), y) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e+81)
		tmp = Float64(fma(-0.5, log(y), x) - z);
	else
		tmp = Float64(fma(Float64(-y), log(y), y) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 7.5e+81], N[(N[(-0.5 * N[Log[y], $MachinePrecision] + x), $MachinePrecision] - z), $MachinePrecision], N[(N[((-y) * N[Log[y], $MachinePrecision] + y), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.49999999999999973e81

   1. Initial program 100.0%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - \left(z + \frac{1}{2} \cdot \log y\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x - \color{blue}{\left(\frac{1}{2} \cdot \log y + z\right)} \]

      2. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - \frac{1}{2} \cdot \log y\right) - z} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \frac{1}{2} \cdot \log y\right) - z} \]

      4. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \log y\right)\right)\right)} - z \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{2} \cdot \log y\right)\right) + x\right)} - z \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \log y} + x\right) - z \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} \cdot \log y + x\right) - z \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2}, \log y, x\right)} - z \]

      9. lower-log.f64 95.3

         \[\leadsto \mathsf{fma}\left(-0.5, \color{blue}{\log y}, x\right) - z \]

   5. Applied rewrites 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5, \log y, x\right) - z} \]

   if 7.49999999999999973e81 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\left(y + \frac{1}{2}\right) \cdot \log y}\right) + y\right) - z \]

      2. *-commutative N/A

         \[\leadsto \left(\left(x - \color{blue}{\log y \cdot \left(y + \frac{1}{2}\right)}\right) + y\right) - z \]

      3. lift-+.f64 N/A

         \[\leadsto \left(\left(x - \log y \cdot \color{blue}{\left(y + \frac{1}{2}\right)}\right) + y\right) - z \]

      4. flip3-+ N/A

         \[\leadsto \left(\left(x - \log y \cdot \color{blue}{\frac{{y}^{3} + {\frac{1}{2}}^{3}}{y \cdot y + \left(\frac{1}{2} \cdot \frac{1}{2} - y \cdot \frac{1}{2}\right)}}\right) + y\right) - z \]

      5. clear-num N/A

         \[\leadsto \left(\left(x - \log y \cdot \color{blue}{\frac{1}{\frac{y \cdot y + \left(\frac{1}{2} \cdot \frac{1}{2} - y \cdot \frac{1}{2}\right)}{{y}^{3} + {\frac{1}{2}}^{3}}}}\right) + y\right) - z \]

      6. un-div-inv N/A

         \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y \cdot y + \left(\frac{1}{2} \cdot \frac{1}{2} - y \cdot \frac{1}{2}\right)}{{y}^{3} + {\frac{1}{2}}^{3}}}}\right) + y\right) - z \]

      7. lower-/.f64 N/A

         \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{y \cdot y + \left(\frac{1}{2} \cdot \frac{1}{2} - y \cdot \frac{1}{2}\right)}{{y}^{3} + {\frac{1}{2}}^{3}}}}\right) + y\right) - z \]

      8. clear-num N/A

         \[\leadsto \left(\left(x - \frac{\log y}{\color{blue}{\frac{1}{\frac{{y}^{3} + {\frac{1}{2}}^{3}}{y \cdot y + \left(\frac{1}{2} \cdot \frac{1}{2} - y \cdot \frac{1}{2}\right)}}}}\right) + y\right) - z \]

      9. flip3-+ N/A

         \[\leadsto \left(\left(x - \frac{\log y}{\frac{1}{\color{blue}{y + \frac{1}{2}}}}\right) + y\right) - z \]

      10. lift-+.f64 N/A

          \[\leadsto \left(\left(x - \frac{\log y}{\frac{1}{\color{blue}{y + \frac{1}{2}}}}\right) + y\right) - z \]

      11. lower-/.f64 99.5

          \[\leadsto \left(\left(x - \frac{\log y}{\color{blue}{\frac{1}{y + 0.5}}}\right) + y\right) - z \]

      12. lift-+.f64 N/A

          \[\leadsto \left(\left(x - \frac{\log y}{\frac{1}{\color{blue}{y + \frac{1}{2}}}}\right) + y\right) - z \]

      13. +-commutative N/A

          \[\leadsto \left(\left(x - \frac{\log y}{\frac{1}{\color{blue}{\frac{1}{2} + y}}}\right) + y\right) - z \]

      14. lower-+.f64 99.5

          \[\leadsto \left(\left(x - \frac{\log y}{\frac{1}{\color{blue}{0.5 + y}}}\right) + y\right) - z \]

   4. Applied rewrites 99.5%

      \[\leadsto \left(\left(x - \color{blue}{\frac{\log y}{\frac{1}{0.5 + y}}}\right) + y\right) - z \]

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(y - \log y \cdot \left(\frac{1}{2} + y\right)\right)} - z \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \color{blue}{\left(y + \left(\mathsf{neg}\left(\log y \cdot \left(\frac{1}{2} + y\right)\right)\right)\right)} - z \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\log y \cdot \left(\frac{1}{2} + y\right)\right)\right) + y\right)} - z \]

      3. *-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{2} + y\right) \cdot \log y}\right)\right) + y\right) - z \]

      4. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{2} + y\right)\right)\right) \cdot \log y} + y\right) - z \]

      5. mul-1-neg N/A

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(\frac{1}{2} + y\right)\right)} \cdot \log y + y\right) - z \]

      6. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(\frac{1}{2} + y\right), \log y, y\right)} - z \]

      7. distribute-lft-in N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot \frac{1}{2} + -1 \cdot y}, \log y, y\right) - z \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2}} + -1 \cdot y, \log y, y\right) - z \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{2} + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}, \log y, y\right) - z \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} - y}, \log y, y\right) - z \]

      11. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} - y}, \log y, y\right) - z \]

      12. lower-log.f64 91.2

          \[\leadsto \mathsf{fma}\left(-0.5 - y, \color{blue}{\log y}, y\right) - z \]

   7. Applied rewrites 91.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 - y, \log y, y\right)} - z \]

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(-1 \cdot y, \log \color{blue}{y}, y\right) - z \]
   9. Step-by-step derivation

   10. Applied rewrites 91.2%

       \[\leadsto \mathsf{fma}\left(-y, \log \color{blue}{y}, y\right) - z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+125}:\\ \;\;\;\;\mathsf{fma}\left(-0.5, \log y, x\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \log y\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.2e+125) (- (fma -0.5 (log y) x) z) (* (- 1.0 (log y)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e+125) {
		tmp = fma(-0.5, log(y), x) - z;
	} else {
		tmp = (1.0 - log(y)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.2e+125)
		tmp = Float64(fma(-0.5, log(y), x) - z);
	else
		tmp = Float64(Float64(1.0 - log(y)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.2e+125], N[(N[(-0.5 * N[Log[y], $MachinePrecision] + x), $MachinePrecision] - z), $MachinePrecision], N[(N[(1.0 - N[Log[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.19999999999999991e125

   1. Initial program 99.9%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x - \left(z + \frac{1}{2} \cdot \log y\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x - \color{blue}{\left(\frac{1}{2} \cdot \log y + z\right)} \]

      2. associate--r+ N/A

         \[\leadsto \color{blue}{\left(x - \frac{1}{2} \cdot \log y\right) - z} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(x - \frac{1}{2} \cdot \log y\right) - z} \]

      4. sub-neg N/A

         \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\frac{1}{2} \cdot \log y\right)\right)\right)} - z \]

      5. +-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{2} \cdot \log y\right)\right) + x\right)} - z \]

      6. distribute-lft-neg-in N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \log y} + x\right) - z \]

      7. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} \cdot \log y + x\right) - z \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2}, \log y, x\right)} - z \]

      9. lower-log.f64 93.3

         \[\leadsto \mathsf{fma}\left(-0.5, \color{blue}{\log y}, x\right) - z \]

   5. Applied rewrites 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5, \log y, x\right) - z} \]

   if 2.19999999999999991e125 < y

   1. Initial program 99.6%

      \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(1 - -1 \cdot \log \left(\frac{1}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(1 - -1 \cdot \log \left(\frac{1}{y}\right)\right) \cdot y} \]

      2. mul-1-neg N/A

         \[\leadsto \left(1 - \color{blue}{\left(\mathsf{neg}\left(\log \left(\frac{1}{y}\right)\right)\right)}\right) \cdot y \]

      3. log-rec N/A

         \[\leadsto \left(1 - \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(\log y\right)\right)}\right)\right)\right) \cdot y \]

      4. remove-double-neg N/A

         \[\leadsto \left(1 - \color{blue}{\log y}\right) \cdot y \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \log y\right) \cdot y} \]

      6. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(1 - \log y\right)} \cdot y \]

      7. lower-log.f64 81.9

         \[\leadsto \left(1 - \color{blue}{\log y}\right) \cdot y \]

   5. Applied rewrites 81.9%

      \[\leadsto \color{blue}{\left(1 - \log y\right) \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y - z\right) + \mathsf{fma}\left(-0.5 - y, \log y, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (- y z) (fma (- -0.5 y) (log y) x)))

C

double code(double x, double y, double z) {
	return (y - z) + fma((-0.5 - y), log(y), x);
}

Julia

function code(x, y, z)
	return Float64(Float64(y - z) + fma(Float64(-0.5 - y), log(y), x))
end

Wolfram

code[x_, y_, z_] := N[(N[(y - z), $MachinePrecision] + N[(N[(-0.5 - y), $MachinePrecision] * N[Log[y], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right) - z} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right)} - z \]

   3. associate--l+ N/A

      \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

   4. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

   5. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right)} + \left(y - z\right) \]

   6. sub-neg N/A

      \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right)\right)} + \left(y - z\right) \]

   7. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right) + x\right)} + \left(y - z\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right) \cdot \log y}\right)\right) + x\right) + \left(y - z\right) \]

   9. distribute-lft-neg-in N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right)\right) \cdot \log y} + x\right) + \left(y - z\right) \]

   10. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right), \log y, x\right)} + \left(y - z\right) \]

   11. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right)}\right), \log y, x\right) + \left(y - z\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{2} + y\right)}\right), \log y, x\right) + \left(y - z\right) \]

   13. distribute-neg-in N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, \log y, x\right) + \left(y - z\right) \]

   14. unsub-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

   15. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2}} - y, \log y, x\right) + \left(y - z\right) \]

   17. lower--.f64 99.8

       \[\leadsto \mathsf{fma}\left(-0.5 - y, \log y, x\right) + \color{blue}{\left(y - z\right)} \]

4. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 - y, \log y, x\right) + \left(y - z\right)} \]

5. Final simplification 99.8%

   \[\leadsto \left(y - z\right) + \mathsf{fma}\left(-0.5 - y, \log y, x\right) \]
6. Add Preprocessing

Alternative 8: 57.1% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x + \left(y - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* 1.0 x) (- y z)))

C

double code(double x, double y, double z) {
	return (1.0 * x) + (y - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 * x) + (y - z)
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 * x) + (y - z);
}

Python

def code(x, y, z):
	return (1.0 * x) + (y - z)

Julia

function code(x, y, z)
	return Float64(Float64(1.0 * x) + Float64(y - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 * x) + (y - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 * x), $MachinePrecision] + N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right) - z} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + y\right)} - z \]

   3. associate--l+ N/A

      \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

   4. lower-+.f64 N/A

      \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right) + \left(y - z\right)} \]

   5. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(x - \left(y + \frac{1}{2}\right) \cdot \log y\right)} + \left(y - z\right) \]

   6. sub-neg N/A

      \[\leadsto \color{blue}{\left(x + \left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right)\right)} + \left(y - z\right) \]

   7. +-commutative N/A

      \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right) \cdot \log y\right)\right) + x\right)} + \left(y - z\right) \]

   8. lift-*.f64 N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right) \cdot \log y}\right)\right) + x\right) + \left(y - z\right) \]

   9. distribute-lft-neg-in N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right)\right) \cdot \log y} + x\right) + \left(y - z\right) \]

   10. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\left(y + \frac{1}{2}\right)\right), \log y, x\right)} + \left(y - z\right) \]

   11. lift-+.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(y + \frac{1}{2}\right)}\right), \log y, x\right) + \left(y - z\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{2} + y\right)}\right), \log y, x\right) + \left(y - z\right) \]

   13. distribute-neg-in N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) + \left(\mathsf{neg}\left(y\right)\right)}, \log y, x\right) + \left(y - z\right) \]

   14. unsub-neg N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

   15. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) - y}, \log y, x\right) + \left(y - z\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2}} - y, \log y, x\right) + \left(y - z\right) \]

   17. lower--.f64 99.8

       \[\leadsto \mathsf{fma}\left(-0.5 - y, \log y, x\right) + \color{blue}{\left(y - z\right)} \]

4. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 - y, \log y, x\right) + \left(y - z\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right)} + \left(y - z\right) \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right) \cdot x} + \left(y - z\right) \]

   2. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right) \cdot x} + \left(y - z\right) \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x} + 1\right)} \cdot x + \left(y - z\right) \]

   4. mul-1-neg N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{\log y \cdot \left(\frac{1}{2} + y\right)}{x}\right)\right)} + 1\right) \cdot x + \left(y - z\right) \]

   5. associate-/l* N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\log y \cdot \frac{\frac{1}{2} + y}{x}}\right)\right) + 1\right) \cdot x + \left(y - z\right) \]

   6. *-commutative N/A

      \[\leadsto \left(\left(\mathsf{neg}\left(\color{blue}{\frac{\frac{1}{2} + y}{x} \cdot \log y}\right)\right) + 1\right) \cdot x + \left(y - z\right) \]

   7. distribute-lft-neg-in N/A

      \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{\frac{1}{2} + y}{x}\right)\right) \cdot \log y} + 1\right) \cdot x + \left(y - z\right) \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\frac{\frac{1}{2} + y}{x}\right), \log y, 1\right)} \cdot x + \left(y - z\right) \]

   9. distribute-neg-frac N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{\mathsf{neg}\left(\left(\frac{1}{2} + y\right)\right)}{x}}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot \left(\frac{1}{2} + y\right)}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   11. lower-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1 \cdot \left(\frac{1}{2} + y\right)}{x}}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   12. distribute-lft-in N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot \frac{1}{2} + -1 \cdot y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2}} + -1 \cdot y}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   14. mul-1-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{\frac{-1}{2} + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   15. unsub-neg N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2} - y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   16. lower--.f64 N/A

       \[\leadsto \mathsf{fma}\left(\frac{\color{blue}{\frac{-1}{2} - y}}{x}, \log y, 1\right) \cdot x + \left(y - z\right) \]

   17. lower-log.f64 86.6

       \[\leadsto \mathsf{fma}\left(\frac{-0.5 - y}{x}, \color{blue}{\log y}, 1\right) \cdot x + \left(y - z\right) \]

7. Applied rewrites 86.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-0.5 - y}{x}, \log y, 1\right) \cdot x} + \left(y - z\right) \]

8. Taylor expanded in x around inf

   \[\leadsto 1 \cdot x + \left(y - z\right) \]
9. Step-by-step derivation

10. Applied rewrites 49.8%

    \[\leadsto 1 \cdot x + \left(y - z\right) \]
11. Add Preprocessing

Alternative 9: 30.1% accurate, 39.3× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- z))

C

double code(double x, double y, double z) {
	return -z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -z
end function

Java

public static double code(double x, double y, double z) {
	return -z;
}

Python

def code(x, y, z):
	return -z

Julia

function code(x, y, z)
	return Float64(-z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -z;
end

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 99.8%

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 25.2

      \[\leadsto \color{blue}{-z} \]

5. Applied rewrites 25.2%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (- (+ y x) z) (* (+ y 0.5) (log y))))

C

double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * log(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((y + x) - z) - ((y + 0.5d0) * log(y))
end function

Java

public static double code(double x, double y, double z) {
	return ((y + x) - z) - ((y + 0.5) * Math.log(y));
}

Python

def code(x, y, z):
	return ((y + x) - z) - ((y + 0.5) * math.log(y))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y + x) - z) - Float64(Float64(y + 0.5) * log(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y + x) - z) - ((y + 0.5) * log(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(y + x), $MachinePrecision] - z), $MachinePrecision] - N[(N[(y + 0.5), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024327 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (- (+ y x) z) (* (+ y 1/2) (log y))))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))